Question

Let $f\left(x\right)=nx+n-[nx+n]+\tan \frac{\pi x}{2}$,
where $\left[x\right]$ is the greatest integer $\le x$ and $n\in N$

It is

• A. a periodic function of period $1$
• B. a periodic function of period $4$
• C. not periodic
• D. a periodic function of period $2$

Answer 1

Answer: (D)

a periodic function of period $2$

$f\left(x\right)=\{nx+n\}+\tan \frac{x\pi }{2}$
Period of $\left\{x\right\}=1$ which is a rational number.
Period of $\tan \frac{\pi x}{2}=\frac{\pi }{\pi }\times 2=2$
Period of $f\left(x\right)=LCM$ of $(2,1)=2$